A parametric study on the dynamic response of planar multibody systems with multiple clearance joints

A general methodology for dynamic modeling and analysis of multibody systems with multiple clearance joints is presented and discussed in this paper. The joint components that constitute a real joint are modeled as colliding bodies, being their behavior influenced by geometric and physical properties of the contacting surfaces. A continuous contact force model, based on the elastic Hertz theory together with a dissipative term, is used to evaluate the intra-joint contact forces. Furthermore, the incorporation of the friction phenomenon, based on the classical Coulomb’s friction law, is also discussed. The suitable contact-impact force models are embedded into the dynamics of multibody systems methodologies. An elementary mechanical system is used to demonstrate the accuracy and efficiency of the presented approach, and to discuss the main assumptions and procedures adopted. Different test scenarios are considered with the purpose of performing a parametric study for quantifying the influence of the clearance size, input crank speed and number of clearance joints on the dynamic response of multibody systems with multiple clearance joints. Additionally, the total computation time consumed in each simulation is evaluated in order to test the computational accuracy and efficiency of the presented approach. From the main results obtained in this study, it can be drawn that clearance size and the operating conditions play a crucial role in predicting accurately the dynamic responses of multibody systems.Fundação para a Ciência e a Tecnologia (FCT

On the contact detection for contact-impact analysis in multibody systems

One of the most important and complex parts of the simulation of multibody systems with contact-impact involves the detection of the precise instant of impact. In general, the periods of contact are very small and, therefore, the selection of the time step for the integration of the time derivatives of the state variables plays a crucial role in the dynamics of multibody systems. The conservative approach is to use very small time steps throughout the analysis. However, this solution is not efficient from the computational view point. When variable time step integration algorithms are used and the pre-impact dynamics does not involve high-frequencies the integration algorithms may use larger time steps and the contact between two surfaces may start with initial penetrations that are artificially high. This fact leads either to a stall of the integration algorithm or to contact forces that are physically impossible which, in turn, lead to post-impact dynamics that is unrelated to the physical problem. The main purpose of this work is to present a general and comprehensive approach to automatically adjust the time step, in variable time step integration algorithms, in the vicinity of contact of multibody systems. The proposed methodology ensures that for any impact in a multibody system the time step of the integration is such that any initial penetration is below any prescribed threshold. In the case of the start of contact, and after a time step is complete, the numerical error control of the selected integration algorithm is forced to handle the physical criteria to accept/reject time steps in equal terms with the numerical error control that it normally uses. The main features of this approach are the simplicity of its computational implementation, its good computational efficiency and its ability to deal with the transitions between non contact and contact situations in multibody dynamics. A demonstration case provides the results that support the discussion and show the validity of the proposed methodology.Fundação para a Ciência e a Tecnologia (FCT

Petrographic characterization of Kentucky coals. Final report. Part VI. The nature of pseudovitrinites in Kentucky coals

Overall average pseudovitrinite content for 1055 eastern Kentucky coal samples is nearly 9% while average percentage of pseudovitrinite for 551 western Kentucky coals is approximately 4%. Examination of variation in pseudovitrinite content relative to rank changes shows uniformity in pseudovitrinite percentages within the 4 to 7 V-type interval for eastern Kentucky coals but a gradual increase in pseudovitrinite content for western Kentucky coals over the same rank interval. Coals from both coal fields show similar, distinct increases in pseudovitrinite percentage in the highest V-type categories. However, it is suggested here that these supposed increases in pseudovitrinite percentages are not real but rather, indicate distinct increase in the brightness of nitrinite resulting from increased alteration of vitrinite beginning at this stage of coalification and continuing into the higher rank stages. This conclusion is reached when it is found that differences between pseudovitrinite and vitrinite reflectance are least in coals at these high rank intervals of Kentucky and, also, when vitrinite particles are often visually observed having brightness equal to that of pseudovitrinite particles. Relation of pseudovitrinite to other sulfur forms and total sulfur in general shows no significant trends, although the relatively high pyritic sulfur content in western Kentucky coals, coupled with relatively low inert percentages suggest the existence of predominantly reducing, or at least non-oxidizing conditions in the Pennsylvanian peat swamps of western Kentucky. Initial work involving Vicker's microhardness testing of coals indicates that microhardness values for pseudovitrinite are higher than those for vitrinite within the same sample regardless of coal rank or coal field from which the sample was collected. 15 references, 9 figures, 9 tables

Dynamics, Friction, And Complementarity Problems

. An overview is presented here of recent work and approaches to solving dynamic problems in rigid body mechanics with friction. It begins with the differential inclusion approach to Coulomb friction where the normal contact force is known. Numerical methods for these differential inclusions commonly lead to linear or nonlinear complementarity problems. Then the measure differential inclusion formulation of rigid body dynamics due to Moreau and others is presented. A novel algorithm for time-stepping for rigid body dynamics is given which avoids the "non-existence" issues that arise in many other formulations. The time-stepping algorithm requires the solution of an NCP at each step. Results on the convergence of the numerical solutions to solutions in the sense of measure differential inclusions are given, and numerical results for an implementation of the method are shown. Key Words. friction, differential inclusions, rigid body dynamics, complementarity problem 1. Introduction. Thi..

Petrographic characterization of Kentucky coals. Quarterly progress report, September-November 1981

The project Petrographic Characterization of Kentucky Coals consists of research in three specific areas of coal petrology: spectral fluorescence of liptinite macerals, properties of semi-inert macerals, and size/form/microlithotype association of pyrite/marcasite. Additional research on the Mannington (No. 4, also known as Mining City and Lewisport) coal will apply techniques developed in the first three areas. Certain suits of coals from other states will also be studied to expand the variability in the samples. Preliminary results are reported

Petrographic characterization of Kentucky coals. Quarterly progress report, March 1982-May 1982

The project Petrographic characterization of Kentucky coals consists of three specific areas of coal petrology: spectral fluorescence of liptinite macerals, properties of semi-inert macerals, and size/form/microlithotype association of pyrite/marcasite. Additional research on the Mannington and Dunbar coals in western Kentucky and the Alma coal zone in eastern Kentucky will apply techniques developed in the first three areas. Suites of coals from other states will also be studied to expand the variability in the sample set